In short: These 25 questions cover 70+ marks out of the 80-mark CBSE Class 12 Maths paper. Each one is derived from the official 2027 SQP pattern, previous year paper trends (2024-2026), and CBSE unit-wise marks allocation. For each question: what it asks, which chapter it comes from, expected marks, section placement, and what the examiner wants to see. Practice every one of these and you walk into the exam hall having already seen 80% of the paper. Also check out our Chemistry expected questions for Class 12.
How This List Was Built
| Source | What We Analysed |
|---|---|
| CBSE Official SQP 2027 | Released Sep 21, 2026. 38 questions across 5 sections. Same pattern as 2025-26. |
| Previous Year Papers (2024-2026) | 3 years of board papers. Identified repeated question types. |
| CBSE Unit-Wise Weightage | Calculus: 35 marks, Vectors and 3D: 14, Algebra: 10, Relations and Functions: 8, Probability: 8, Linear Programming: 5. See the full chapter-wise weightage breakdown. |
| SQP Marking Scheme | Step-wise marks allocation. |
Unit-Wise Expected Marks Distribution
| Unit | Chapters | Expected Marks | Questions in This List |
|---|---|---|---|
| Relations and Functions | Relations, Functions, Inverse Trig | 8 | #1-2 |
| Algebra | Matrices, Determinants | 10 | #3-5 |
| Calculus | Continuity, Derivatives, Integrals, Applications, Differential Equations | 35 | #6-16 |
| Vectors and 3D Geometry | Vectors, 3D Lines and Planes | 14 | #17-20 |
| Linear Programming | LP Problems | 5 | #21 |
| Probability | Conditional, Bayes', Distributions | 8 | #22-25 |
| Total | 80 | 25 questions |
Relations and Functions (8 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 1 | Show that a given relation (e.g., R on Z defined by (a,b) ∈ R iff a-b is divisible by n) is an equivalence relation. Find the equivalence class of a given element. | LA | 5 | D |
| 2 | Find the value of an inverse trigonometric expression. Example: tan⁻¹(1) + cos⁻¹(-1/2) + sin⁻¹(-1/2). OR Prove an inverse trig identity. | MCQ / SA | 1-3 | A / C |
What the examiner wants
- Q1: Prove reflexive (show (a,a) ∈ R for all a), symmetric (if (a,b) ∈ R then (b,a) ∈ R), and transitive (if (a,b) ∈ R and (b,c) ∈ R then (a,c) ∈ R). Each property = 1-2 marks. Finding equivalence class = 1 mark.
- Q2: Know the principal value ranges: sin⁻¹ ∈ [-π/2, π/2], cos⁻¹ ∈ [0, π], tan⁻¹ ∈ (-π/2, π/2). Use standard angle values.
PYQ track record
| Year | Equivalence relation appeared? | Inverse trig appeared? |
|---|---|---|
| 2024 | Yes (5 marks) | Yes (MCQ + 3 marks) |
| 2025 | Yes (5 marks) | Yes (MCQ) |
| 2026 | Yes (5 marks) | Yes (3 marks) |
| 2027 SQP | Yes | Yes |
Verdict: Equivalence relation is a guaranteed 5-mark question. Memorize the proof structure.
Algebra — Matrices and Determinants (10 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 3 | Find the inverse of a 3×3 matrix using elementary row operations OR using the adjoint method (A⁻¹ = adj(A)/ | A | ). | LA |
| 4 | Using properties of determinants, prove a given identity. Example: Prove that a determinant with rows involving (a+b+c) factors out to give a specific expression. | SA | 3 | C |
| 5 | Solve a system of linear equations using the matrix method (AX = B, X = A⁻¹B). | SA / LA | 3-5 | C / D |
What the examiner wants
- Q3: If using row operations, show each step clearly: R₂ → R₂ - R₁ etc. The transformation steps carry most of the marks. If using adjoint method: find |A| first, then cofactor matrix, then adjoint, then A⁻¹.
- Q4: Apply row/column operations to simplify. Take common factors out. Do NOT expand the determinant directly — that wastes time and marks.
- Q5: Write A, X, B matrices clearly. Find A⁻¹. Multiply. State the solution.
Calculus — Continuity and Differentiability (8 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 6 | Find dy/dx for an implicit function, parametric function, or logarithmic differentiation. Example: If y = xˣ, find dy/dx. OR If x = a(cos t + t sin t), y = a(sin t - t cos t), find dy/dx. | SA | 3 | C |
| 7 | Verify Rolle's Theorem or Mean Value Theorem for a given function on a given interval. | MCQ / VSA | 1-2 | A / B |
What the examiner wants
- Q6: For logarithmic differentiation, take log on both sides FIRST, then differentiate. For parametric: dy/dx = (dy/dt)/(dx/dt). Show every step.
- Q7: State the conditions (continuity on [a,b], differentiability on (a,b), f(a)=f(b) for Rolle's). Verify each condition. Find the value of c.
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Calculus — Application of Derivatives (5 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 8 | Find the maximum or minimum value of a function. Typical: maximise area/volume given a constraint (e.g., open box from a square sheet, cylinder inscribed in cone). | LA | 5 | D |
| 9 | Find the rate of change of a quantity. Example: rate at which area of a circle is changing when radius is increasing at a given rate. | MCQ / VSA | 1-2 | A / B |
What the examiner wants
- Q8: Express the quantity to be optimised as a function of ONE variable. Differentiate. Set dy/dx = 0. Find critical points. Use second derivative test to confirm maximum or minimum. Each step is clearly marked.
- Q9: Direct chain rule application. dA/dt = dA/dr × dr/dt. Show the substitution.
PYQ pattern
Optimisation problems (box, cylinder, window) appear in Section D every year. The themes rotate between: open box from square sheet, fencing a rectangular garden, and maximising volume of an inscribed cylinder.
Calculus — Integrals (12 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 10 | Evaluate an indefinite integral using: partial fractions, substitution, or integration by parts (ILATE). Example: ∫(2x+3)/(x²+3x+2) dx OR ∫x²eˣ dx OR ∫eˣ(sinx + cosx) dx. For a complete list of integration formulas and types, see our Integration formulas guide. | SA | 3 | C |
| 11 | Evaluate a definite integral using properties: ∫₀ᵃ f(x)dx = ∫₀ᵃ f(a-x)dx. Example: ∫₀^(π/2) log(sinx) dx type problems. | SA / LA | 3-5 | C / D |
| 12 | Find the area bounded by curves using integration. Example: area between a parabola and a line, or area between two curves. | LA | 5 | D |
What the examiner wants
- Q10: Identify the METHOD first (partial fractions for rational, substitution for composed functions, ILATE for products). Write the method name explicitly — examiners look for this.
- Q11: State the property being used. Apply it. Simplify. This is a common 3-5 mark question.
- Q12: Draw a ROUGH SKETCH (1 mark). Identify intersection points. Set up the integral with correct limits. Evaluate. The sketch carries marks even if your final answer is wrong.
PYQ pattern
Integration questions appear in EVERY section of the paper (MCQ, SA, LA, Case-Based). Area under curves is always a 5-mark question in Section D.
Calculus — Differential Equations (5 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 13 | Solve a first-order linear differential equation (dy/dx + Py = Q) using the integrating factor method. | SA / LA | 3-5 | C / D |
| 14 | Form a differential equation from a given general solution. OR find the order and degree of a differential equation. | MCQ / VSA | 1-2 | A / B |
What the examiner wants
- Q13: Convert to standard form dy/dx + Py = Q. Find IF = e^(∫P dx). Multiply both sides. Integrate. Write the general solution. Every step = marks.
- Q14: For forming a DE: differentiate the general solution as many times as there are arbitrary constants. Eliminate the constants.
Vectors and 3D Geometry (14 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 15 | Find the angle between two vectors, or the projection of one vector on another using dot product. OR find a unit vector perpendicular to two given vectors using cross product. | VSA / SA | 2-3 | B / C |
| 16 | Find the shortest distance between two skew lines. OR find the equation of a line through a given point and perpendicular to two given lines. | LA | 5 | D |
| 17 | Find the equation of a plane through three given points, or through a point and perpendicular to a given line. | SA | 3 | C |
| 18 | Find the distance of a point from a plane. OR find the angle between a line and a plane. | VSA / SA | 2-3 | B / C |
Key formulas to memorize cold
| Formula | Expression | When to use |
|---|---|---|
| Dot product | a⃗·b⃗ = | a⃗ |
| Cross product magnitude | a⃗×b⃗ | |
| Shortest distance (skew lines) | d = | (a⃗₂-a⃗₁)·(b⃗₁×b⃗₂) |
| Distance: point to plane | d = | ax₁+by₁+cz₁+d |
| Plane equation | r⃗·n⃗ = d or ax+by+cz = d | Equation of plane |
PYQ track record
Shortest distance between skew lines has appeared in Section D as a 5-mark question in 2 out of 3 years. The equation of a plane question appears every year in Section C.
Linear Programming (5 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 19 | Solve a linear programming problem graphically. Maximise or minimise Z = ax + by subject to constraints. Find the feasible region and evaluate Z at each corner point. | LA | 5 | D |
What the examiner wants
- Convert word problem into constraints (1 mark).
- Plot all constraint lines on a graph (1 mark).
- Shade the feasible region correctly (1 mark).
- Identify corner points (coordinates) (1 mark).
- Evaluate Z at each corner point and state maximum/minimum (1 mark).
PYQ pattern
LP always appears as a 5-mark question. The themes rotate between: manufacturing (tables and chairs), diet (vitamins and minerals), and transport (cost minimisation). Practice all three types.
Probability (8 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 20 | Bayes' Theorem application. Given prior probabilities and conditional probabilities, find the posterior probability. Typical: defective items from factories, disease testing, bag-and-ball problems. | LA / Case-Based | 5 | D / E |
| 21 | Find the probability distribution of a random variable (mean and variance). Given a random variable X with possible values, construct the probability distribution table. | SA | 3 | C |
| 22 | Conditional probability: find P(A | B) using the formula P(A∩B)/P(B). | MCQ / VSA | 1-2 |
| 23 | Multiplication rule or independent events. Show that two events are independent or find the probability of "at least one" event. | MCQ / VSA | 1-2 | A / B |
What the examiner wants
- Q20: Define events clearly (E₁, E₂, A). State Bayes' formula. Substitute values. Show every fraction calculation. This is the highest-value probability question.
- Q21: List all values of X. Find P(X = xᵢ) for each. Verify ΣP = 1. Calculate E(X) = ΣxᵢP(xᵢ). Calculate Var(X) = E(X²) - [E(X)]².
PYQ track record
Bayes' Theorem has appeared in EVERY board paper from 2024-2026 — either in Section D (5 marks) or Section E (case-based, 4 marks). It is the most predictable probability question.
Case-Based Questions — Section E (12 Marks)
| # | Expected Question | Type | Marks | Section |
|---|---|---|---|---|
| 24 | Integration-based case study. Real-world scenario (area of land, profit function, cost-revenue). Sub-questions on: finding the integral, evaluating at limits, interpreting the result. | Case-Based | 4 | E |
| 25 | Probability or 3D Geometry case study. Scenario-based (quality control, sports tournament, construction). Sub-questions testing different concepts from the same scenario. | Case-Based | 4 | E |
What the examiner wants
- Read the ENTIRE case first before answering any sub-question.
- Sub-questions are independent but use the same data — do them in order.
- Each sub-question is typically 1-2 marks. Show working even for 1-mark questions.
30-Day Practice Plan
| Week | Focus | Questions from This List |
|---|---|---|
| Week 1 | Calculus — Integrals, Derivatives, Applications | #6-12 (practice each type 3 times) |
| Week 2 | Algebra + Relations + LP | #1-5, #19 (matrix inverse + determinant proofs) |
| Week 3 | Vectors, 3D, Probability | #15-18, #20-23 (Bayes' + skew lines) |
| Week 4 | Case-Based + Full Papers | #24-25 + solve 3 full mock papers timed |
Section-Wise Time Strategy on Exam Day
| Section | Questions | Marks | Time | Strategy |
|---|---|---|---|---|
| A (MCQ + A-R) | 20 | 20 | 30 min | Quick. Use elimination for tough MCQs. |
| B (VSA) | 5 | 10 | 15 min | Direct formulas. Show working. |
| E (Case-Based) | 3 | 12 | 25 min | Do BEFORE Section D. Easier marks per minute. |
| C (SA) | 6 | 18 | 30 min | Step-wise working. Integration, determinants, vectors. |
| D (LA) | 4 | 20 | 45 min | Hardest. Equivalence relation, matrix inverse, area under curves, LP or Bayes'. |
| Review | — | — | 15 min | Recheck MCQs, verify integration calculations in D. |
Key strategy: Tackle Section E before D. Case-based questions carry 12 marks and are typically easier than Section D long answers.
Frequently Asked Questions
Q1. Are these 25 questions enough for the full 80-mark paper? These 25 cover every high-probability question TYPE. The actual paper has 38 questions (many MCQs test minor variations). If you master all 25, you are prepared for 70+ marks.
Q2. Which chapters are most important for scoring 90+? Integration (12+ marks), Probability (8 marks), 3D Geometry (8+ marks), and Matrices (5+ marks). These four areas account for 35+ marks and are the most predictable.
Q3. Is NCERT enough for Class 12 Maths? NCERT + NCERT Exemplar covers 85% of what you need. For the remaining 15% (tricky MCQs and case-based questions), solve 3-4 previous year papers and the official SQP.
Q4. Should I attempt all questions or leave some? There is no negative marking in board exams. Attempt EVERY question. Even a partially correct answer (correct formula, correct first step) scores marks. Never leave a question blank.
Q5. What is the most common mistake in Class 12 Maths board exam? Skipping steps in integration and differentiation. Examiners follow a step-marking scheme — if you jump from the problem to the answer, you lose 2-3 marks even if the answer is correct. For more on how examiners mark and how to write answers for maximum marks, read our answer sheet presentation guide.
Q6. How similar will the actual paper be to this list? Based on PYQ analysis, 20-22 of these 25 question types appear in every board paper. The remaining 3-5 marks come from MCQ variations that test basic formula recall. Check our detailed SQP vs actual paper analysis for the full comparison. And make sure your time management strategy for the 3-hour paper is ready before exam day.
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